A circle centered at A with a radius of 1 and a circle centered at B with a radius of 4 are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. The radius of the third circle is

**Answer Choices**

A. \dfrac{1}{3}

B. \dfrac{2}{5}

C. \dfrac{5}{12}

D. \dfrac{4}{9}

E. \dfrac{1}{2}